Question

If a constant number of moles of a gas is at a pressure of 1.35 atm and has a volume of 23.8 L at a temperature of 205.1 K then what is the final volume of the gas if the pressure changes to 2.84 atm and the temperature rises to 233.4 K?

Answer 1

To solve this problem, we can use the combined gas law equation:

P1V1 / T1 = P2V2 / T2

Where:
P1 = initial pressure = 1.35 atm
V1 = initial volume = 23.8 L
T1 = initial temperature = 205.1 K
P2 = final pressure = 2.84 atm
V2 = final volume (unknown)
T2 = final temperature = 233.4 K

Now we can plug in the values and solve for V2:

(1.35 atm * 23.8 L) / 205.1 K = (2.84 atm * V2) / 233.4 K

(32.13) / 205.1 = 2.84 * V2 / 233.4

0.1568 = 2.84 * V2 / 233.4

Cross multiply:
0.1568 * 233.4 = 2.84 * V2
36.58 = 2.84 * V2

Divide by 2.84:
V2 = 12.90 L

Therefore, the final volume of the gas is 12.90 L.